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Emmeans & effects packages: Post-hoc tests for Tweedie glmmTMB model

3 messages · John Fox, Millar, Niall

Original
John Fox
# 
Dear Niall,

I've not seen applications of GLMMs using the Tweedie Family, but don't see why that should matter. The "effects" computed by the functions in the effects package are linear functions of the estimated fixed-effects parameters, and their asymptotic standard errors are computed from the estimated covariance matrix of the fixed effects. The default (asymptotic) confidence intervals are computed pointwise and so don't adjust for simultaneous inference, but there is an option to compute Scheffe intervals.

By the way, the fixed-effects part of your model is more compactly Shoot.weight ~ N.Level*Rhiz*Species.

I hope this helps,
 John

--------------------------------------
John Fox, Professor Emeritus
McMaster University
Hamilton, Ontario, Canada
Web: socialsciences.mcmaster.ca/jfox/
3 days later
Millar, Niall
# 
Dear John,

Thanks very much for reply. I'd just like to clarify a few points and make sure I understand. Do you mean that the effects package calculates these asymptotic confidence intervals by assuming that the distribution of the parameters (not the data) is normal? If so, can I then generate hypothesis tests with these confidence intervals by assuming some uncertainty in the parameter values?

Thanks,
-Niall
John Fox
# 
Dear Niall,
Yes, the estimated fixed-effects coefficients and the estimated effects, which are linear combinations of the estimated coefficients, are asymptotically normal, and the confidence intervals reported are either based on the normal or t-distribution, depending on the model. 

But it's not obvious to me that the point-wise confidence intervals for the effects correspond to hypotheses that you want to test. The object returned by Effect(), however, contains not only the estimated effects, their standard errors, and confidence limits, but also their full covariance matrix. Consequently, you should be able to formulate a Wald test for *any* linear combination of the effects of interest, or even, by the delta method, a test for a nonlinear function of the fixed effects.

Best,
 John